Actually China is trying convincing Italy to be a part of OBOR.
https://www.portseurope.com/italian-ports-are-strategic-for-chinas-one-belt-one-road-initiative-pm/
http://www.xinhuanet.com/english/2017-05/17/c_136289886.htm
Italy's economy has been in somewhat of a decline and this opportunity could rejuvenate it. With Britain's exit from the EU, it has sort of set a precedent that if EU and it's regulations aren't working for a country, that country can set its own course. So Italy doesn't necessarily have to cave in to EU's pressure. Turkey is right next door to Italy too...and with China eyeing the Mediterranean ports/routes, it would be a no brainer for Turkey to join in.
This initiative is barely starting out...once the trade starts in full swing along CPEC/OBOR...a lot of countries would be willing to join.